Simplified space vector modulation method for multi-level converter

ABSTRACT

The disclosure discloses a simplified space vector modulation method for multi-lever converters, and relates to the field of space vector modulation methods for multilevel converters, which solves problems that a redundant on-off state is greatly increased along with increase of a number of levels in a traditional SVM technology, and SVM is difficult to realize due to calculation of the redundant on-off state and selection of a proper on-off state. The method comprises the following steps of: step 1: establishing a vector expression; step 2: establishing a reference vector trajectory model; step 3: respectively representing reference signals and level signals by coordinate components of a reference vector and a basic vector and corresponding component sums; step 4: constructing a star-connected multilevel converter; step 5: sampling a phase voltage reference vector trajectory model of the star-connected multilevel converter, and synthesizing the reference vector.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of International Patent ApplicationNo. PCT/CN2019/094457 with a filing date of Jul. 3, 2019, designatingthe United States, now pending, and further claims priority to ChinesePatent Application No. 201910426666.6 with a filing date of May 21,2019. The content of the aforementioned applications, including anyintervening amendments thereto, are incorporated herein by reference.

TECHNICAL FIELD

The present disclosure relates to the field of space vector modulationmethods for multi-level converter, and more particularly, to asimplified space vector modulation method for multi-level converters.

BACKGROUND

At present, Carrier Phase Shifted Modulation (CPS) and Nearest LevelModulation (NLM) are mostly used in high-power multi-level converterdevices. With the number of cascaded sub-modules increasing, carrierphase shifted modulation has higher requirement on carriersynchronization, and needs a lot of hardware resources and strict logicsequence. Therefore, a multi-level converter using CPS has a smallnumber of levels, which limits the improvement of a voltage level of aconverter. In nearest level modulation technology, a voltage trackingerror is large when the number of levels is small, and a large number ofharmonic components are widely distributed in a wide frequency band in aspectrum of an output voltage. Moreover, there is no characteristicharmonic, thus being very difficult to design a filter. In summary, thecarrier phase shifted modulation and the nearest level modulation bothhave a special level modulation adaptation range. Compared with theabove two modulation methods, Space Vector Modulation (SVM) is easilyexpanded to multi-level converters with any topology and any number oflevels. Under the same DC voltage, a DC voltage utilization rate of theSVM is 15.47% higher than that of the carrier modulation, and the SVMhas advantages of a small voltage tracking error, a low switchingfrequency, a small switching loss and the like.

SVM strategy is widely used in three-level and five-level converters,but is not common in industrial applications of high-voltage high-powerconverters. The reason is that with the number of levels increasing in aSVM technology, 2/3 conversion is needed, and redundant switching statesare greatly increased. Calculation of the redundant switching states andselection of proper switching states greatly increase difficulty inimplement the SVM algorithm. Therefore, a simplified space vectormodulation method for a multi-level converter is urgently needed in amarket to help people solve existing problems.

SUMMARY

The present disclosure is intended to provide a simplified space vectormodulation method for a multi-level converter, based on a relationshipbetween a phase voltage and a line voltage of a star-connectedconverter, a reference vector calculated from phase voltage referencesignals is directly used as a line voltage reference vector. Moreover,two line-voltage levels are used as two components of the space vector,with a sum of these two components being a third line-voltage level.These three components are directly used as switching state signals ofthe control line voltages. The proposed space vector modulation methodavoids 2/3 conversion and does not need to calculate redundant switchingstates, which greatly simplifies a SVM algorithm and ensures that acommon-mode voltage of the converter is zero at the any time.

In order to achieve the above objective, the present disclosure providesthe following technical solutions: a simplified space vector modulationmethod for a multi-level converter comprises the following steps of:

step 1: an expression of a basic vector V_(αβ)(v_(α),v_(β))corresponding to a phase voltage in a traditional Cartesian coordinatesystem (referred to as an α-β, coordinate system) being:

${\begin{bmatrix}v_{\alpha} \\v_{\beta}\end{bmatrix} = \begin{bmatrix}{\frac{1}{3}( {{2v_{a}} - v_{b} - v_{c}} )} \\{{\frac{\sqrt{3}}{3}( {v_{b} - v_{c}} )}\mspace{34mu}}\end{bmatrix}},$

wherein v_(α) and v_(β) represent coordinate components corresponding tothe basic vector V_(αβ), v_(a), v_(b) and v_(c) respectively representlevels corresponding to three phase voltages of a multi-level converter,(v_(a), v_(b), v_(c)) is called a switching state corresponding to thebasic vector V_(αβ), and for an n-level converter, v_(a), v_(b), v_(c)∈[(n−1)(n−2), . . . , 2, 1, 0] and

a reference vector V_(rαβ)(v_(rα),v_(rβ)) calculated according to phasevoltage reference signals in the α-β coordinate system being:

${\begin{bmatrix}v_{r\; \alpha} \\v_{r\; \beta}\end{bmatrix} = {\frac{\sqrt{3}}{3}{{m( {n - 1} )}\begin{bmatrix}{\cos \mspace{14mu} \omega \; t} \\{\sin \mspace{14mu} \omega \; t}\end{bmatrix}}}};$

wherein v_(rα) and v_(rβ), represent coordinate components correspondingto the reference vectors V_(rαβ);

step 2: rotating a coordinate axis of an α-β plane counterclockwise by45 degrees and scaleding an axial proportion to obtain an α′-β′coordinate system, and establishing a reference vector trajectory model;

a basic vector V′(v_(α)′,v_(β)′) in the coordinate system α′-β′ being:

${\begin{bmatrix}v_{\alpha}^{\prime} \\v_{\beta}^{\prime}\end{bmatrix} = {{\begin{bmatrix}1 & 0 & {- 1} \\{- 1} & 1 & 0\end{bmatrix}\begin{bmatrix}v_{a} \\v_{b} \\v_{c}\end{bmatrix}} = \begin{bmatrix}{{v_{a} - v_{c}}\mspace{20mu}} \\{{- v_{a}} + v_{b}}\end{bmatrix}}},$

wherein v_(α)′ and v_(β)′ represent coordinate components correspondingto the basic vector V′;

a reference vector V_(r)′(v_(rα)′,v_(rβ)′) calculated according to phasevoltage reference signals in the α′-β′ coordinate system being:

${\begin{bmatrix}v_{r\; \alpha}^{\prime} \\v_{r\; \beta}^{\prime}\end{bmatrix} = {\frac{m( {n - 1} )}{2}\begin{bmatrix}{{{\sqrt{3}\cos \mspace{14mu} \omega \; t} + {\sin \mspace{14mu} \omega \; t}}\mspace{14mu}} \\{{{- \sqrt{3}}\cos \mspace{14mu} \omega \; t} + {\sin \mspace{14mu} \omega \; t}}\end{bmatrix}}},$

wherein v_(rα)′ and v_(rβ)′ represent coordinate componentscorresponding to the reference vector V_(r)′;

the reference vector trajectory model in the α′-β′ coordinate systembeing:

${{( \frac{v_{r\; \alpha}^{\prime} + v_{r\; \beta}^{\prime}}{m( {n - 1} )} )^{2} + ( \frac{v_{r\; \alpha}^{\prime} - v_{r\; \beta}^{\prime}}{\sqrt{3}{m( {n - 1} )}} )^{2}} = 1};$${m = \frac{\sqrt{3}U_{r}}{( {n - 1} )E}};$

step 3: in the α′-β′ coordinate system, respectively representing linevoltage reference signals −u_(rca), −u_(rab) and u_(rbc) by thecoordinate components v_(rα)′ and v_(rβ)′ of the reference vector V_(r)′and the sum of the two components v_(rα)′+V_(rβ)′, and respectivelyrepresenting line voltage level signals −v_(ca), −v_(ab) and v_(bc) bythe coordinate components V_(α)′ and v_(β)′ of the basic vector V′ andthe sum of the two coordinate components v_(α)′+v_(β)′:

$\{ {\begin{matrix}{{v_{r\; \alpha}^{\prime} = {{u_{ra} - u_{rc}} = {- u_{rca}}}}\mspace{40mu}} \\{{v_{r\; \beta}^{\prime} = {{{- u_{ra}} + u_{rb}} = {- u_{rab}}}}\mspace{20mu}} \\{{v_{r\; \alpha}^{\prime} + v_{r\; \beta}^{\prime}} = {{u_{rb} - u_{rc}} = u_{rbc}}}\end{matrix},} $

wherein u_(rab), u_(rbc) and u_(rca) respectively represent referencesignals of the three line voltages;

${{\begin{bmatrix}{v_{\alpha}^{\prime}\mspace{50mu}} \\{v_{\beta}^{\prime}\mspace{50mu}} \\{v_{\alpha}^{\prime} + v_{\beta}^{\prime}}\end{bmatrix}==\begin{bmatrix}{{v_{a} - v_{c}}\mspace{20mu}} \\{{- v_{a}} + v_{b}} \\{{v_{b} - v_{c}}\mspace{20mu}}\end{bmatrix}} = \begin{bmatrix}{- v_{ca}} \\{- v_{ab}} \\{v_{bc}\mspace{20mu}}\end{bmatrix}},$

wherein v_(ab), v_(bc) and v_(ca) respectively represent levelscorresponding to the three line voltages,v_(ab),v_(bc),v_(ca)∈[±n,±(n−1), . . . , ±2,±1, 0], and each linevoltage outputs 2n+1 levels;

step 4: constructing a new star-connected multi-level converter, so thatline voltage reference signals of the new star-connected multi-levelconverter are the same as line voltage reference signals of a controlleddelta-connected multi-level converter;

step 5: sampling a reference vector trajectory model of the constructedstar-connected multi-level converter, calculating three basic vectorsclosest to the sampled reference vector V_(r)′, using the three basicvectors as equivalent basic vectors, the three equivalent basic vectorsforming a sector triangle, and synthesizing the reference vector byusing the three equivalent basic vectors;

step 6: calculating duty cycles of the equivalent basic vectors whichsynthesize the sampled reference vector by using a volt-second balanceprinciple:

when the reference vector is located in Sector-I:

$\{ {\begin{matrix}{{t_{1} = {T_{S}( {1 + v_{\alpha}^{\prime} - v_{r\; \alpha}^{\prime}} )}}\mspace{110mu}} \\{{t_{2} = {T_{S}( {1 + v_{\beta}^{\prime} - v_{r\; \beta}^{\prime}} )}}\mspace{110mu}} \\{t_{3} = {T_{S}( {v_{r\; \alpha}^{\prime} + v_{r\; \beta}^{\prime} - v_{\alpha}^{\prime} - v_{\beta}^{\prime} - 1} )}}\end{matrix},} $

wherein t₁, t₂ and t₃ respectively represent duty cycles of vectors V₁′,V₂′ and V₃′, and T_(S) represents a sampling period;

when the reference vector is located in Sector-II:

$\{ {\begin{matrix}{t_{0} = {T_{S}( {1 + v_{\alpha}^{\prime} + v_{\beta}^{\prime} - v_{r\; \alpha}^{\prime} - v_{r\; \beta}^{\prime}} )}} \\{{t_{1} = {T_{S}( {v_{r\; \alpha}^{\prime} - v_{\alpha}^{\prime}} )}}\mspace{155mu}} \\{{t_{3} = {T_{S}( {v_{r\; \beta}^{\prime} - v_{\beta}^{\prime}} )}}\mspace{149mu}}\end{matrix},} $

wherein t₀, t₁ and t₃ respectively represent duty cycles of vectors V₀′,V₁′ and V₃′; and

step 7: using the components of the equivalent basic vector of the phasevoltage reference vector of the star-connected multi-level converter andthe sum of the two components as switching states for controlling a linevoltage of the delta-connected multi-level converter.

Preferably, in step 5, the sector triangles formed by three adjacentbasic vectors are all isosceles right triangles, and the length of theright sides of the isosceles right triangle is unit 1, there are onlytwo types of sector triangles: Sector-I and Sector-II, and the basicvectors forming the Sector-I- and Sector-II comprise V₀′(v_(α)′,V_(β)′), V₁′(v_(α)′+1, V_(β)′) V₂′(v_(α)′+1,v_(β)′+1) andV₃′(v_(α)′,v_(β)′+1)

and

$\{ {\begin{matrix}{v_{\alpha}^{\prime} = {{floor}( v_{r\; \alpha}^{\prime} )}} \\{v_{\beta}^{\prime} = {{floor}( v_{r\; \beta}^{\prime} )}}\end{matrix},} $

wherein floor(*) represents a rounding down function;

in a first case: wherein (v_(rα)′−v_(α)′)+(v_(rβ)′−v_(β)′)≥1, thereference vector is located in the Sector-I, and the reference vector issynthesized by using the vectors V₁′(v_(α)′+1,v_(β)′)V₂′(v_(α)′+1,v_(β)′+1) and V₃′(v_(α)′,v_(β)′+1) and

in a second case: wherein (v_(rα)′−v_(α)′)+v_(rβ)′−v_(β)′)<1, thereference vector is located in Sector-II, and the reference vector issynthesized by using the vectors V₀′(v_(α)′,v_(β)′),V₁′(v_(α)′+1,v_(β)′) and V₃′(v_(α)′,v_(β)′+1).

Preferably, the reference vector is located in Sector-I, when thereference voltage vector V_(r)′ is synthesized by using V₁′, V₂′ and V₃′according to the volt-second balance principle, the switching states ofthe corresponding delta-connected multi-level converter are respectively(−v_(β)′,v_(α)′+v_(β)′+1,−(v_(α)′+1)),(−(v_(β)′+1),v_(α)′+v_(β)′+2,−(v_(α)′+1)) and(−(v_(β)′+1),v_(α)′+v_(β)′+1,−v_(α)′):

(1) during the duty cycle of the basic vector V₁′, −v_(β)′, vα′+v_(β)′+1and −(v_(α)′+1) are respectively used as control signals of a phase AB,a phase BC and a phase CA of the controlled delta-connected multi-levelconverter;

(2) during the duty cycle of the basic vector V₂′, −(v_(β)′+1),v_(α)′+v_(β)′+2 and −(v_(α)′+1) are respectively used as control signalsof the phase AB, the phase BC and the phase CA of the controlleddelta-connected multi-level converter;

(3) during the duty cycle of the basic vector V₃′, −(v_(β)′+1),v_(α)′+v_(β)′+1 and −v_(α)′ are respectively used as control signals ofthe phase AB, the phase BC and the phase CA of the controlleddelta-connected multi-level converter.

Preferably, the reference vector is located in Sector-II, when thereference voltage vector V_(r)′ is synthesized by using V₀′, V₁′ and V₃′according to the volt-second balance principle, the switching states ofthe corresponding delta-connected multi-level converter are respectively(−v_(β)′,v_(α)′+v_(β)′,−v_(α)′), (−v_(β)′,v_(α)′+v_(β)′+1,−(v_(α)′+1))and (−(v_(β)′+1), v_(α)′+v_(β)′+1,−v_(α)′):

(1) during the duty cycle of the basic vector V₀′, −v_(β)′,v_(α)′+v_(β)′ and −v_(α)′ are respectively used as control signals ofthe phase AB, the phase BC and the phase CA of the controlleddelta-connected multi-level converter;

(2) during the duty cycle of the basic vector V₁′, −v_(β)′,v_(α)′+v_(β)′+1 and −(v_(α)′+1) are respectively used as control signalsof the phase AB, the phase BC and the phase CA of the controlleddelta-connected multi-level converter;

(3) during the duty cycle of the basic vector V₃′, −(v_(β)′+1),v_(α)′+v_(β)′+1 and −v_(α)′ are respectively used as control signals ofthe phase AB, the phase BC and the phase CA of the controlleddelta-connected multi-level converter.

Preferably, a sum of the three components of the switching states at anymoment is 0, which means that an output common-mode voltage of athree-phase converter is 0.

Preferably, the switching states are used as the control signals of theline voltage of the delta-connected multi-level converter, wherein thereare two corresponding components that differ by one level in any twoswitching states, which means that during one sampling period of thereference vector, when the switching states are switched, a switchingpath is closed by the four-segment switching method with any one of thethree switching states as a starting point, when the reference vector islocated in Sector-I, the switching sequence of the switching state isprovided with three modes:

mode (1):(−v_(β)′,v_(α)′+v_(β)′+1,−(v_(α)′+1))→(−(v_(β)′+1),v_(α)′+v_(β)′+2,−(v_(α)′+1))→(−(v_(β)′+1),v_(α)′+v_(β)′+1,−v_(α)′)→(−v_(β)′,v_(α)′+v_(β)′+1,−(v_(α)′+1)),corresponding to a duty cycle t₁/2→t₂→t→t₁/2,

mode (2):(−(v_(β)′+1),v_(α)′+v_(β)′+2,−(v_(α)′+1))→(−(v_(β)′+1),v_(α)′+v_(β)′+1,−v_(α)′)→(−v_(β)′,v_(α)′+v_(β)′+1,−(v_(α)′+1))→(−(v_(β)′+1),α′+v_(β)′+2,−(v_(α)′+1)),corresponding to a duty cycle t₂/2→t₃→t₁→t₂/2,

mode (3):(−(v_(β)′+1),v_(α)′+v_(β)′+1,−v_(α)′)→(−v_(β),v_(α)′+v_(β)′+1,−(v_(α)′+1))→(−(v_(β)′+1),v_(α)′+v_(β)′+2,−(v_(α)′+1))→(−(v_(β)′+1),v_(α)′+v_(β)′+1,−v_(α)′),corresponding to a duty cycle t₃/2→t₁→t₂→t₃/2,

any one of the three modes is selected; and

when the reference vector is located in Sector-II, the switchingsequence of the switching state is provided with three modes:

mode (1):(−v_(β)′,v_(α)′+v_(β)′,−v_(α)′)→(−v_(β)′,v_(α)′+v_(β)′+1,−(v_(α)′+1))→(−(v_(β)′+1),v_(α)′+v_(β)′+1,−v_(α)′)→(−v_(β)′,v_(α)′+v_(β)′,−v_(α)′),corresponding to a duty cycle t₀/2→t₁→t₃-t₀/2,

mode (2):(−v_(β)′,v_(α)′+v_(β)′+1,−(v_(α)′+1))→(−(v_(β)′+1),v_(α)′+v_(β)′+1,−v_(α)′)→(−v_(β)′,v_(α)′+v_(β)′,−v_(α)′)→(−v_(β)′v_(α)′+v_(β)′+1,−(v_(α)′+1)),corresponding to a duty cycle t₁/2→t₃→t₀→t₁/2,

mode (3):(−(v_(β)′+1),v_(α)′+v_(β)′+1,−v_(α)′)→(−v_(β)′,v_(α)′+v_(β)′,−v_(α)′)→(−v_(β)′,v_(α)′+v_(β)′+1,−(v_(α)′+1))→(−(v_(β)′+1),v_(α)′+v_(β)′+1,−v_(α)′),corresponding to a duty cycle t₃/2→t₀→t₁→t₃/2,

any one of the three modes is selected.

Preferably, each phase in the delta-connected multi-level converter isformed by cascading 2k H-bridge sub-modules, an output line voltage has4k+1 levels, an output phase voltage of the star-connected multi-levelconverter has 2k+1 levels, and an output line voltage has 4k+1 levels,which means that a number of levels of the output line voltage of thestar-connected converter formed by cascading k H-bridge sub-modules isequal to a number of levels of the output line voltage of thedelta-connected converter formed by cascading 2k H-bridge sub-modules.

Preferably, in the α′-β′, coordinate system, the star-connectedconverter formed by cascading 2k H-bridge sub-modules is modulated bythe simplified space vector modulation method for the multi-levelconverter according to the following steps:

step 1: imagining a star-connected converter, wherein each phase of theconverter is formed by cascading k H-bridge sub-modules;

step 2: dividing the phase voltage reference signals of the controlledconverter by √{square root over (3)} to obtain phase voltage referencesignals of the imaged converter; and

step 3: in the α′-β′ coordinate system, sampling a phase voltagereference vector trajectory model of the imaged converter, synthesizingthe reference vector by using three equivalent basic vectors on thesector triangle, and using the coordinate components of the equivalentbasic vector and the sum of the two coordinate components as switchingstate signals of three phases of the controlled converter to realizespace vector modulation.

Compared with the prior art, the present disclosure has the beneficialeffects as follows.

By analyzing physical meanings of the reference vector and the basicvector in a 45-degree rotating coordinate system, in the coordinatesystem, the coordinate components of the reference vector calculatedaccording to the phase voltage reference signals and the sum of the twocomponents are equivalent to the line voltage reference signals, and thecoordinate components of the basic vector and the sum of the twocomponents are equivalent to the switching state signals for controllingthe line voltage. On this basis, a relationship between the phasevoltage and the line voltage of the star-connected converter is used todirectly use the coordinate components of the reference vectorcalculated according to the phase voltage reference signals and the sumof the two components as the line voltage reference signals and directlyuse the coordinate components of the equivalent basic vector whichsynthesizes the reference vector and the sum of the two components asthe switching state signals for controlling the line voltage, and themethod avoids 2/3 conversion which must be completed in a traditionalspace vector modulation algorithm and does not need to calculateredundant switching states, greatly simplifies a SVM algorithm andensures that a common-mode voltage is zero, thus improving an outputvoltage performance of the converter, being conveniently popularized andapplied to a multi-level converter with any topology without increasinga difficulty in realizing the algorithm.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagram showing space vector distribution of a five-levelconverter under an α-β coordinate and a reference vector trajectoryaccording to the present disclosure;

FIG. 2 is a diagram showing a transformation relationship between anα′-β′ coordinate system and an α-β coordinate system according to thepresent disclosure;

FIG. 3 is a diagram showing space vector distribution of a five-levelconverter under an α′-β′ coordinate and a reference vector trajectoryaccording to the present disclosure;

FIG. 4 is a diagram showing locating of a sector triangle and asynthesis principle of a reference vector according to the presentdisclosure;

FIG. 5A and FIG. 5B are principle diagrams of a triangle-connectedH-bridge-cascaded multilevel converter according to the presentdisclosure; wherein FIG. 5A shows the multilevel converter comprises thetriangle-connected converter formed by cascading the H-bridgesub-modules; FIG. 5B shows each phase in the figure is formed bycascading 2k H-bridge sub-modules; and

FIG. 6 is a principle diagram of a star-connected H-bridge-cascadedmulti-level converter according to the present disclosure.

DETAILED DESCRIPTION

The technical solutions in the embodiments of the present disclosure areclearly and completely described with reference to the accompanyingdrawings in the embodiments of the present disclosure. Apparently, thedescribed embodiments are only some but not all of the embodiments ofthe present disclosure.

With reference to FIG. 1 to FIG. 6, according to an embodiment providedby the present disclosure, a simplified space vector modulation methodfor a multi-level converter comprises the following steps.

In step 1, expressions of a basic vector and a reference vector in atraditional Cartesian coordinate system (referred to as an α-βcoordinate system) are provided:

wherein reference signals of a phase voltage of the converter are:

$\{ {\begin{matrix}{{u_{ra} = {U_{r}\mspace{14mu} \cos \mspace{14mu} \omega \; t\text{/}E}}\mspace{79mu}} \\{u_{rb} = {U_{r}\mspace{14mu} {\cos ( {{\omega \; t} - {2\pi \text{/}3}} )}\text{/}E}} \\{u_{rc} = {U_{r}\mspace{14mu} {\cos ( {{\omega \; t} + {2\pi \text{/}3}} )}\text{/}E}}\end{matrix}\quad} $

wherein U_(r) represents a phase voltage amplitude expected to beoutputted by the converter, which is also called a reference voltageamplitude, and E represents a direct current voltage corresponding to aunit level.

In the α-β coordinate system, according to a definition of a spacevector, a reference vector V_(rαβ)(v_(r)α,v_(r)β) is:

$\begin{matrix}{\begin{matrix}{V_{r\; {\alpha\beta}} = {\frac{2}{3}\lbrack {u_{ra} + {e^{j\frac{2\pi}{3}}u_{rb}} + {( e^{j\frac{2\pi}{3}} )^{2}u_{rc}}} \rbrack}} \\{= {\frac{1}{3}\lbrack {( {{2u_{ra}} - u_{rb} - u_{rc}} ) + {j\sqrt{3}( {u_{rb} - u_{rc}} )}} \rbrack}} \\{= {{U_{r}( {{\cos \mspace{14mu} \omega \; t} + {j\mspace{14mu} \sin \mspace{14mu} \omega \; t}} )}\text{/}E}} \\{= {v_{r\; \alpha} + {jv}_{r\; \beta}}}\end{matrix},} & (1)\end{matrix}$

wherein v_(rα) and v_(rβ) represent coordinate components correspondingto the reference vector V_(rαβ).

A relationship between a basic vector V_(αβ)(v_(α),v_(β)) and levels ofthree phase voltages is:

$\begin{matrix}{{\begin{bmatrix}v_{\alpha} \\v_{\beta}\end{bmatrix} = \begin{bmatrix}{\frac{1}{3}( {{2v_{a}} - v_{b} - v_{c}} )} \\{{\frac{\sqrt{3}}{3}( {v_{b} - v_{c}} )}\mspace{34mu}}\end{bmatrix}},} & (2)\end{matrix}$

wherein v_(α) and v_(β) represent coordinate components corresponding tothe basic vector V_(αβ), v_(a), v_(b) and v_(c) respectively representlevels of three phase voltages of a multi-level converter, (v_(a),v_(b), v_(c)) is called a switching state corresponding to the basicvector V_(αβ), and for an n-level converter, v_(a),v_(b),v_(c) ∈[(n−1),(n−2), . . . , 2, 1, 0]

A reference vector trajectory of a five-level converter under an α-βcoordinate and space vector distribution are established, wherein threeadjacent vectors form a sector triangle, as shown in FIG. 1.

A maximum value U_(rmax) of a reference voltage amplitude of an n-levelconverter is:

$\begin{matrix}{U_{r\mspace{14mu} \max} = {\frac{\sqrt{3}}{3}( {n - 1} ){E.}}} & (3)\end{matrix}$

A direct current voltage has a maximum utilization rate at the moment,which is set to be 1, and an actual utilization rate of the directcurrent voltage is changed according to a change of the referencevoltage amplitude. An actual reference voltage amplitude is:

U _(r) =mU _(rmax)  (4),

wherein m is a modulation coefficient, a change of m leads to a changeof a radius of a trajectory circle of the reference vector, a value of mreflects the utilization rate of the direct current voltage, and

$m = {\frac{\sqrt{3}U_{r}}{( {n - 1} )E}.}$

Formulas (3) and (4) are substituted into a formula (1) to obtain:

$\begin{matrix}{\begin{bmatrix}v_{r\; \alpha} \\v_{r\; \beta}\end{bmatrix} = {\frac{\sqrt{3}}{3}{{{m( {n - 1} )}\begin{bmatrix}{\cos \mspace{14mu} \omega \; t} \\{\sin \mspace{14mu} \omega \; t}\end{bmatrix}}.}}} & (5)\end{matrix}$

In step 2, a coordinate axis of an α-β plane is rotated counterclockwiseby 45 degrees and an axial proportion is compressed to obtain an α′-β′coordinate system, the expression of the basic vector in the α′-β′coordinate system is calculated, and a reference vector trajectory modelis established. A coordinate transformation principle is shown in FIG.2:

$\begin{matrix}{{\begin{bmatrix}v_{\alpha}^{\prime} \\v_{\beta}^{\prime}\end{bmatrix} = {{C\begin{bmatrix}v_{\alpha} \\v_{\beta}\end{bmatrix}} = {C_{r}{C_{c}\begin{bmatrix}v_{\alpha} \\v_{\beta}\end{bmatrix}}}}},} & (6)\end{matrix}$

wherein C^(r) is a 45-degree counterclockwise rotation transformationmatrix,

${C_{r} = {\begin{bmatrix}{\cos \frac{\pi}{4}} & {\sin \frac{\pi}{4}} \\{{- \sin}\frac{\pi}{4}} & {\cos \frac{\pi}{4}}\end{bmatrix} = \begin{bmatrix}\frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} \\{- \frac{\sqrt{2}}{2}} & \frac{\sqrt{2}}{2}\end{bmatrix}}},$

C_(c) is an axial compression transformation matrix, and

$C_{c} = {\begin{bmatrix}{3\sqrt{2}\text{/}2} & 0 \\0 & {\sqrt{6}\text{/}2}\end{bmatrix}.}$

A formula (2) is substituted into a formula (6) to obtain a basic vectorV′(v_(α)′,v_(β)′) in the α′-β′ coordinate system, which is:

$\begin{matrix}{{\begin{bmatrix}v_{\alpha}^{\prime} \\v_{\beta}^{\prime}\end{bmatrix} = {{\begin{bmatrix}1 & 0 & {- 1} \\{- 1} & 1 & 0\end{bmatrix}\begin{bmatrix}v_{a} \\v_{b} \\v_{c}\end{bmatrix}} = \begin{bmatrix}{{v_{a} - v_{c}}\mspace{20mu}} \\{{- v_{a}} + v_{b}}\end{bmatrix}}},} & (7)\end{matrix}$

wherein v_(α)′ and v_(β)′ represent coordinate components correspondingto the basic vector V′.

A reference vector V_(r)′(v_(rα)′,v_(rβ)′) in the α′-β′ coordinatesystem is:

$\begin{matrix}{{\begin{bmatrix}v_{r\; \alpha}^{\prime} \\v_{r\; \beta}^{\prime}\end{bmatrix} = {\frac{m( {n - 1} )}{2}\begin{bmatrix}{{{\sqrt{3}\cos \mspace{14mu} \omega \; t} + {\sin \mspace{14mu} \omega \; t}}\mspace{14mu}} \\{{{- \sqrt{3}}\cos \mspace{14mu} \omega \; t} + {\sin \mspace{14mu} \omega \; t}}\end{bmatrix}}},} & (8)\end{matrix}$

wherein v_(rα)′ and v_(rβ) represent coordinate components correspondingto the reference vector V_(r)′.

The reference vector trajectory model in the α′-β′ coordinate system is:

$\begin{matrix}{{( \frac{v_{r\; \alpha}^{\prime} + v_{r\; \beta}^{\prime}}{m( {n - 1} )} )^{2} + ( \frac{v_{r\; \alpha}^{\prime} - v_{r\; \beta}^{\prime}}{\sqrt{3}{m( {n - 1} )}} )^{2}} = 1.} & (9)\end{matrix}$

In step 3, in the α′-β′ coordinate system, line voltage referencesignals −u_(rca), −u_(rab) and u_(rbc) are respectively represented bythe coordinate components v_(rα)′ and v_(rβ)′ of the reference vectorV_(r)′ and the sum of two components v_(rα)′+v_(rβ)′, and line voltagelevel signals −v_(ca), −v_(ab) and v_(bc) are respectively representedby the coordinate components v_(α)′ and v_(β)′ of the basic vector V′and the sum of two coordinate components v_(α)′+v_(β)′.

According to a formula (7),

$\begin{matrix}\{ {\begin{matrix}{{v_{r\; \alpha}^{\prime} = {{u_{ra} - u_{rc}} = {- u_{rca}}}}\mspace{40mu}} \\{{v_{r\; \beta}^{\prime} = {{{- u_{ra}} + u_{rb}} = {- u_{rab}}}}\mspace{20mu}} \\{{v_{r\; \alpha}^{\prime} + v_{r\; \beta}^{\prime}} = {{u_{rb} - u_{rc}} = u_{rbc}}}\end{matrix},}  & (10)\end{matrix}$

wherein u_(rab), u_(rbc) and u_(rca) respectively represent referencesignals of the three line voltages, and a formula (10) is consistentwith a formula (8).

$\begin{matrix}{{{\begin{bmatrix}{v_{\alpha}^{\prime}\mspace{50mu}} \\{v_{\beta}^{\prime}\mspace{50mu}} \\{v_{\alpha}^{\prime} + v_{\beta}^{\prime}}\end{bmatrix}==\begin{bmatrix}{{v_{a} - v_{c}}\mspace{20mu}} \\{{- v_{a}} + v_{b}} \\{{v_{b} - v_{c}}\mspace{20mu}}\end{bmatrix}} = \begin{bmatrix}{- v_{ca}} \\{- v_{ab}} \\{v_{bc}\mspace{20mu}}\end{bmatrix}},} & (11)\end{matrix}$

wherein v_(ab), v_(bc) and v_(ca) respectively represent levelscorresponding to the three line voltages, v_(ab), v_(bc),v_(ca)∈[±n,±(n−1), . . . , ±2,±1, 0], and each line voltage outputs 2n+1levels.

A reference vector trajectory of a five-level converter under an α′-β′coordinate and space vector distribution are shown in FIG. 3.

In step 4, a new star-connected multi-level converter is constructed, sothat line voltage reference signals of the new star-connectedmulti-level converter are the same as line voltage reference signals ofa controlled delta-connected multi-level converter.

In step 5, a phase voltage reference vector trajectory model of theconstructed star-connected multi-level converter is sampled, three basicvectors closest to the sampled reference vector V_(r)′ are calculated,and the three basic vectors are used as equivalent basic vectors. Thethree equivalent basic vectors form a sector triangle, and the referencevector is synthesized by using the three equivalent basic vectors.

The sector triangles formed by three adjacent basic vectors are allisosceles right triangles, and a length of a right side of the isoscelesright triangle is unit 1. The sector triangles are in Sector-I andSector-II, and a locating principle of the sector triangle used is shownin FIG. 4.

Four vectors V₀′(v_(α)′,v_(β)′), V₁′(v_(α)′+¹,v_(β)′),V₂′(v_(α)′+1,v_(β)′+1) and V₃′(v_(α)′,v_(β)′+1) form a unit square,

and

$\begin{matrix}\{ {\begin{matrix}{v_{\alpha}^{\prime} = {{floor}( v_{r\; \alpha}^{\prime} )}} \\{v_{\beta}^{\prime} = {{floor}( v_{r\; \beta}^{\prime} )}}\end{matrix},}  & (12)\end{matrix}$

wherein floor(*) represents a rounding down function.

(v_(rα)′−v_(α)′)+(v_(rβ)′−v_(β)′)≥1, wherein the reference vector islocated in the Sector-I, and the reference vector is synthesized byusing the vectors V₁′(v_(α)′+1,v_(β)′), V₂′(v_(α)′+1,v_(β)′+1) andV₃′(v_(α)′,v_(β)′+1)

(v_(rα)′−v_(α)′)+(v_(rβ)′−v_(β)′)<1, wherein the reference vector islocated in the Sector-II, and the reference vector is synthesized byusing the vectors V₀′(v_(α)′,v_(β)′) V₁′(v_(α)′+1,v_(β)′) andV₃′(v_(α)′,v_(β)′+1)

In step 6, duty cycles of the equivalent basic vectors which synthesizethe sampled reference vector are calculated by using a volt-secondbalance principle.

When the reference vector is located in a Sector-I, according to thevolt-second balance principle,

$\begin{matrix}\{ {\begin{matrix}{{{V_{1}^{\prime}t_{1}} + {V_{2}^{\prime}t_{2}} + {V_{3}^{\prime}t_{3}}} = {V_{r}^{\prime}T_{S}}} \\{{{t_{1} + t_{2} + t_{3}} = T_{S}}\mspace{110mu}}\end{matrix},}  & (13)\end{matrix}$

wherein ^(t) 1, ^(t) 2 and ^(t) 3 respectively represent duty cycles ofvectors V₂ ′ and V₃′and T_(s) represents a sampling period.

$\begin{matrix}\{ {\begin{matrix}{{t_{1} = {T_{S}( {1 + v_{\alpha}^{\prime} - v_{r\; \alpha}^{\prime}} )}}\mspace{110mu}} \\{{t_{2} = {T_{S}( {1 + v_{\beta}^{\prime} - v_{r\; \beta}^{\prime}} )}}\mspace{115mu}} \\{t_{3} = {T_{S}( {v_{r\; \alpha}^{\prime} + v_{r\; \beta}^{\prime} - v_{\alpha}^{\prime} - v_{\beta}^{\prime} - 1} )}}\end{matrix},}  & (14)\end{matrix}$

when the reference vector is located in a Sector-II, according to thevolt-second balance principle,

$\begin{matrix}\{ {\begin{matrix}{{{V_{0}^{\prime}t_{0}} + {V_{1}^{\prime}t_{1}} + {V_{3}^{\prime}t_{3}}} = {V_{r}^{\prime}T_{S}}} \\{{{t_{0} + t_{1} + t_{3}} = T_{S}}\mspace{104mu}}\end{matrix},}  & (15)\end{matrix}$

wherein t₀, t₁ and t₃ respectively represent duty cycles of vectors V₀′,V₁′ and V₃′, and

$\begin{matrix}\{ {\begin{matrix}{t_{0} = {T_{S}( {1 + v_{\alpha}^{\prime} + v_{\beta}^{\prime} - v_{r\; \alpha}^{\prime} - v_{r\; \beta}^{\prime}} )}} \\{{t_{1} = {T_{S}( {v_{r\; \alpha}^{\prime} - v_{\alpha}^{\prime}} )}}\mspace{155mu}} \\{{t_{3} = {T_{S}( {v_{r\; \beta}^{\prime} - v_{\beta}^{\prime}} )}}\mspace{149mu}}\end{matrix}.}  & (16)\end{matrix}$

In step 7, the components of the equivalent basic vector of the phasevoltage reference vector of the star-connected multi-level converter andthe sum of the two components are used as switching states forcontrolling a line voltage of the delta-connected multi-level converter.

Further, the multi-level converter comprises the delta-connectedconverter formed by cascading the H-bridge sub-modules (as shown in FIG.5) and the star-connected converter formed by cascading the H-bridgesub-modules (as shown in FIG. 6). Taking the delta-connected converterformed by cascading the H-bridge sub-modules as an example, each phasein the figure is formed by cascading 2k H-bridge sub-modules (as shownin FIG. 5(b)). An input voltage of the H-bridge sub-modules is E and anoutput voltage of the H-bridge sub-modules is u_(sm). When S₁ and S₄ areon and S₂ and S₃ are off, u_(sm)=E. When S₁ and S₄ are off and S₂ and S₃are on, u_(sm)=−E. When S₁ and S₃ are on and S₂ and S₄ are off, or whenS₁ and S₃ are off and S₂ and S₄ are on, u_(sm)=0. An output line voltageof the delta-connected converter with each phase formed by cascading 2ksub-modules has 4k+1 levels.

An output phase voltage of the star-connected converter with each phaseformed by cascading k sub-modules has 2k+1 levels, and an output linevoltage has 4k+1 levels, which means that a number of levels of theoutput line voltage of the star-connected converter formed by cascadingk H-bridge sub-modules is equal to a number of levels of the output linevoltage of the delta-connected converter formed by cascading 2k H-bridgesub-modules.

Line voltage reference signals outputted by the delta-connectedconverter are equal to line voltage reference signals outputted by thestar-connected converter, and according to a formula (10):

$\begin{matrix}\{ {\begin{matrix}{{u_{rAB} = {u_{rab} = {- v_{r\; \beta}^{\prime}}}}\mspace{40mu}} \\{u_{rBC} = {u_{rbc} = {v_{r\; \alpha}^{\prime} + v_{r\; \beta}^{\prime}}}} \\{{u_{rCA} = {u_{rca} = {- v_{r\; \alpha}^{\prime}}}}\mspace{40mu}}\end{matrix},}  & (17)\end{matrix}$

wherein r_(rAB), u_(rBC) and u_(rCA) respectively represent the linevoltage reference signals of the delta-connected converter, and u_(rab),u_(rbc) and u_(rca) respectively represent the line voltage referencesignals of the star-connected converter.

According to a formula (11):

$\begin{matrix}{{\begin{bmatrix}v_{AB}^{\prime} \\v_{BC}^{\prime} \\v_{CA}^{\prime}\end{bmatrix} = {\begin{bmatrix}v_{ab}^{\prime} \\v_{bc}^{\prime} \\v_{ca}^{\prime}\end{bmatrix} = \begin{bmatrix}{{- v_{\beta}^{\prime}}\mspace{31mu}} \\{v_{\alpha}^{\prime} + v_{\beta}^{\prime}} \\{{- v_{\alpha}^{\prime}}\mspace{34mu}}\end{bmatrix}}},} & (18)\end{matrix}$

wherein v_(AB)′, v_(BC)′ and v_(CA)′ respectively represent outputlevels corresponding to line voltages of the delta-connected converter,(v_(AB)′,v_(BC)′,v_(CA)′) refers to a switching state of thedelta-connected converter, and v_(ab)′, v_(bc)′ and v_(ca)′ respectivelyrepresent output levels corresponding to line voltages of thestar-connected converter.

For the star-connected converter, any reference vectorV_(r)′(v_(rα)′,v_(rβ)′) is synthesized by using three vectorsV_(H)′(v_(αh)′,v_(βh)′), V_(I)′(V_(αi)′, v_(βi)′) and V_(J)′(v_(αj)′,v_(βj)′) and:

$\begin{matrix}\{ {\begin{matrix}{{{\begin{bmatrix}v_{\alpha \; h}^{\prime} \\v_{\beta \; h}^{\prime}\end{bmatrix}t_{h}} + {\begin{bmatrix}v_{\alpha \; i}^{\prime} \\v_{\beta \; i}^{\prime}\end{bmatrix}t_{i}} + {\begin{bmatrix}v_{\alpha \; j}^{\prime} \\v_{\beta \; j}^{\prime}\end{bmatrix}t_{j}}} = {\begin{bmatrix}v_{r\; \alpha}^{\prime} \\v_{r\; \beta}^{\prime}\end{bmatrix}T_{S}}} \\{{{t_{h} + t_{i} + t_{j}} = T_{S}}\mspace{250mu}}\end{matrix},}  & (19)\end{matrix}$

wherein t_(h), t_(i) and t_(j) respectively represent duty cycles ofvectors V_(H)′, V_(I)′ and V_(J)′.

According to a formula (19):

$\begin{matrix}\{ {\begin{matrix}{{{\begin{bmatrix}{{- v_{\beta \; h}^{\prime}}\mspace{40mu}} \\{v_{\alpha \; h}^{\prime} + v_{\beta \; h}^{\prime}} \\{{- v_{\alpha \; h}^{\prime}}\mspace{40mu}}\end{bmatrix}t_{h}} + {\begin{bmatrix}{{- v_{\beta \; i}^{\prime}}\mspace{34mu}} \\{v_{\alpha \; i}^{\prime} + v_{\beta \; i}^{\prime}} \\{{- v_{\alpha \; i}^{\prime}}\mspace{34mu}}\end{bmatrix}t_{i}} + {\begin{bmatrix}{{- v_{\beta \; j}^{\prime}}\mspace{40mu}} \\{v_{\alpha \; j}^{\prime} + v_{\beta \; j}^{\prime}} \\{{- v_{\alpha \; j}^{\prime}}\mspace{40mu}}\end{bmatrix}t_{j}}} = {\begin{bmatrix}{{- v_{r\; \beta}^{\prime}}\mspace{40mu}} \\{v_{r\; \alpha}^{\prime} + v_{r\; \beta}^{\prime}} \\{{- v_{r\; \alpha}^{\prime}}\mspace{40mu}}\end{bmatrix}T_{S}}} \\{{{t_{h} + t_{i} + t_{j}} = T_{S}}\mspace{495mu}}\end{matrix},}  & (20)\end{matrix}$

(−v_(βh)′,v_(αh)′+v_(βh)′,−v_(αh)′), (−v_(βi)′,v_(αi)′,−v_(αi)′) and(−v_(βj)′,v_(αj)′+v_(βj)′,−v_(αj)′) respectively represent switchingstates of the line voltage of the star-connected converter correspondingto the basic vectors V_(H)′, V_(I)′ and V_(J)′. According to formulas(17) and (18), the switching states of the line voltage of thestar-connected converter may be used as the switching state signals ofthe line voltage of the delta-connected converter, which means that theline voltage of the delta-connected converter may be directly modulatedby using the switching states of the line voltage obtained by thestar-connected converter.

Taking the reference vector V_(r)′ shown in FIG. 4 as an example, thereference vector V_(r)′ is located in Sector-I, V_(r)′ is synthesized byusing V₁′, V₂′ and V₃′, and:

$\begin{matrix}{{{\begin{bmatrix}{v_{\alpha}^{\prime} + 1} \\{v_{\beta}^{\prime}\mspace{40mu}}\end{bmatrix}t_{1}} + {\begin{bmatrix}{v_{\alpha}^{\prime} + 1} \\{v_{\beta}^{\prime} + 1}\end{bmatrix}t_{2}} + {\begin{bmatrix}{v_{\alpha}^{\prime}\mspace{40mu}} \\{v_{\beta}^{\prime} + 1}\end{bmatrix}t_{3}}} = {\begin{bmatrix}v_{r\; \alpha}^{\prime} \\v_{r\; \beta}^{\prime}\end{bmatrix}{T_{S}.}}} & (21)\end{matrix}$

A formula (21) is linearly transformed to obtain:

$\begin{matrix}{{\begin{bmatrix}{{- v_{\beta}^{\prime}}\mspace{76mu}} \\{v_{\alpha}^{\prime} + v_{\beta}^{\prime} + 1} \\{{- ( {v_{\alpha}^{\prime} + 1} )}\mspace{14mu}}\end{bmatrix}t_{1}} + {\begin{bmatrix}{{- ( {v_{\beta}^{\prime} + 1} )}\mspace{14mu}} \\{v_{\alpha}^{\prime} + v_{\beta}^{\prime} + 2} \\{{- ( {v_{\alpha}^{\prime} + 1} )}\mspace{14mu}}\end{bmatrix}t_{2}} + {\quad{{\begin{bmatrix}{{- ( {v_{\beta}^{\prime} + 1} )}\mspace{14mu}} \\{v_{\alpha}^{\prime} + v_{\beta}^{\prime} + 1} \\{{- v_{\alpha}^{\prime}}\mspace{76mu}}\end{bmatrix}t_{3}} = {{\begin{bmatrix}{{- v_{r\; \beta}^{\prime}}\mspace{40mu}} \\{v_{r\; \alpha}^{\prime} + v_{r\; \beta}^{\prime}} \\{{- v_{r\; \alpha}^{\prime}}\mspace{40mu}}\end{bmatrix}T_{S}} = {\begin{bmatrix}u_{rAB}^{\prime} \\u_{rBC}^{\prime} \\u_{rCA}^{\prime}\end{bmatrix}{T_{S}.}}}}}} & (22)\end{matrix}$

According to (22), a line voltage reference signal(u_(rAB)′,u_(rBC)′,u_(rCA)′) is synthesized by using switching states(−v_(β)′,v_(α)′+v_(β)′+1,−(v_(α)′+1)),(−(v_(β)′+1),v_(α)′+v_(β)′+2,−(v_(α)′+1)) and(−(v_(β)′+1),v_(α)′+v_(β)′+1,−v_(α)′) according to a time-sharing systemto control the line voltage of the delta-connected converter.

If the reference vector V_(r)′ is located in Sector-II, V_(r)′ issynthesized by using V₀′, V₁′ and V₃′, and:

$\begin{matrix}{{{\begin{bmatrix}v_{\alpha}^{\prime} \\v_{\beta}^{\prime}\end{bmatrix}t_{0}} + {\begin{bmatrix}{v_{\alpha}^{\prime} + 1} \\{v_{\beta}^{\prime}\mspace{40mu}}\end{bmatrix}t_{1}} + {\begin{bmatrix}{v_{\alpha}^{\prime}\mspace{40mu}} \\{v_{\beta}^{\prime} + 1}\end{bmatrix}t_{3}}} = {\begin{bmatrix}v_{r\; \alpha}^{\prime} \\v_{r\; \beta}^{\prime}\end{bmatrix}{T_{S}.}}} & (23)\end{matrix}$

A formula (23) is linearly transformed to obtain:

$\begin{matrix}{{\begin{bmatrix}{{- v_{\beta}^{\prime}}\mspace{31mu}} \\{v_{\alpha}^{\prime} + v_{\beta}^{\prime}} \\{{- v_{\alpha}^{\prime}}\mspace{34mu}}\end{bmatrix}t_{0}} + {\begin{bmatrix}{{- v_{\beta}^{\prime}}\mspace{76mu}} \\{v_{\alpha}^{\prime} + v_{\beta}^{\prime} + 1} \\{{- ( {v_{\alpha}^{\prime} + 1} )}\mspace{14mu}}\end{bmatrix}t_{1}} + {\quad{{\begin{bmatrix}{{- ( {v_{\beta}^{\prime} + 1} )}\mspace{14mu}} \\{v_{\alpha}^{\prime} + v_{\beta}^{\prime} + 1} \\{{- v_{\alpha}^{\prime}}\mspace{76mu}}\end{bmatrix}t_{3}} = {{\begin{bmatrix}{{- v_{r\; \beta}^{\prime}}\mspace{40mu}} \\{v_{r\; \alpha}^{\prime} + v_{r\; \beta}^{\prime}} \\{{- v_{r\; \alpha}^{\prime}}\mspace{40mu}}\end{bmatrix}T_{S}} = {\begin{bmatrix}u_{rAB}^{\prime} \\u_{rBC}^{\prime} \\u_{rCA}^{\prime}\end{bmatrix}{T_{S}.}}}}}} & (24)\end{matrix}$

According to (24), a line voltage reference signal (u_(rAB)′,u_(rBC)′,u_(rCA)′) is synthesized by using switching states(−v_(β)′,v_(α)′+v_(β)′,−v_(α)′), (−v_(β)′,v_(α)′+v_(β)′+1,−(v_(α)′+1))and (−(v_(β)′+1),v_(α)′+v_(β)′+1,−v_(α)′) according to volt-secondbalance principle to control the line voltage of the delta-connectedconverter.

Further, a sum of the three components of the switching states at anymoment is 0, which means that an output common-mode voltage of athree-phase converter is 0.

Further, the line voltage reference signals are synthesized by theswitching states, wherein two components of every two of three switchingstates differ by one level, and during one sampling period of thereference vector, when the switching states are switched, a switchingpath is closed by a four-segment switching method with any one of thethree switching states as a starting point,

The reference vector V_(r)′ is located in Sector-I, and a switchingsequence of a switching state is provided with three modes:

mode (1):(−v_(β)′,v_(α)′+v_(β)′+1,−(v_(α)′+1))→(−(v_(β)′+1),v_(α)′+v_(β)′+2,−(v_(α)′+1))→(−(v_(β)′+1),v_(α)′+v_(β)′+1,−v_(α)′)→(−v_(β)′,v_(α)′+v_(β)′+1,−(v_(α)′+1)),corresponding to a duty cycle t₁/2→t₂→t₃→t₁/2,

mode (2):(−(v_(β)′+1),v_(α)′+v_(β)′+2,−(v_(α)′+1))→(−(v_(β)′+1),v_(α)′+v_(β)′+1,−v_(α)′)→(−v_(β)′,v_(α)′+v_(β)′+1,−(v_(α)′+1))→(−(v_(β)′+1),v_(α)′+v_(β)′+2,−(v_(α)′+1)),corresponding to a duty cycle t₂/2→t₃→t₁→t₂/2,

mode (3):(−(v_(β)′+1),v_(α)′+v_(β)′+1,−v_(α)′)→(−v_(β)′,v_(α)′+v_(β)′+1,−(v_(α)′+1))→(−(v_(β)′+1),v_(α)′v_(β)′+2,−(v_(α)′+1))→(−(v_(β)′+1),v_(α)′+v_(β)′+1,−v_(α)′),corresponding to a duty cycle t₃/2→t₁→t₂→t₃/2,

any one of the three modes is selected.

The reference vector V_(r)′ is located in the II-type sector triangle,and the switching sequence of the switching state is provided with threemodes:

mode (1):(−v_(β)′,v_(α)′+v_(β)′,−v_(α)′)→(−v_(β)′,v_(α)′+v_(β)′+1,−(v_(α)′+1))→(−(v_(β)′+1),v_(α)′+v_(β)′+1,−v_(α)′)→(−v_(β)′,v_(α)′+v_(β)′,−v_(α)′),corresponding to a duty cycle t₀/2→t₁→t₃→t₀/2,

mode (2):(−v_(β)′,v_(α)′+v_(β)+1,−(v_(α)′+1))→(−(v_(β)′+1),v_(α)′+v_(β)′+1,−v_(α)′)→(−v_(β)′,v_(α)′+v_(β)′,−v_(α)′)→(−v_(β)′v_(α)′+v_(β)′+1,−(v_(α)′+1)),corresponding to a duty cycle t₁/2→t₃→t₀→t₁/2,

mode (3):(−(v_(β)′+1),v_(α)′+v_(β)′+1,−v_(α)′)→(−v_(β)′,v_(α)′+v_(β)′,−v_(α)′)→(−v_(β)′,v_(α)′+v_(β)′+1,−(v_(α)′+1))→(−(v_(β)′+1),v_(α)′+v_(β)′+1,−v_(α)′),corresponding to a duty cycle t₃/2→t₀→t₁→t₃/2,

any one of the three modes is selected.

It can be known from the above deduction that in the α′-β′ coordinatesystem, as long as a number of cascaded sub-modules of thestar-connected converter is a half number of cascaded sub-modules of thedelta-connected converter, and the line voltage reference signalsoutputted by the star-connected converter are equal to the line voltagereference signals outputted by the delta-connected converter, thencoordinate components of a phase voltage reference vector of thestar-connected converter and a sum of the two components may be used asthe reference vector signals of the line voltage of the delta-connectedconverter, and coordinate components of the basic vector calculated bythe star-connected converter according to a phase voltage and a sum ofthe two components are used as the switching states corresponding to theline voltage of the delta-connected converter, thus realizing the spacevector modulation of the delta-connected converter.

Further, in the α′-β′ coordinate system, the simplified space vectormodulation method for the multi-level converter proposed by the presentdisclosure may be used to modulate the star-connected converter formedby cascading 2k H-bridge sub-modules, and a specific implementationmethod is as follows. Firstly, a star-connected converter is imagined(each phase of the converter is formed by cascading k H-bridgesub-modules). Secondly, the phase voltage reference signals of thecontrolled converter are divided by √{square root over (3)} to obtainphase voltage reference signals of the imaged converter. Thirdly, in theα′-β′ coordinate system, a phase voltage reference vector trajectorymodel of the imaged converter is sampled, the reference vector issynthesized by using three equivalent basic vectors on the sectortriangle, the coordinate components of the equivalent basic vector andthe sum of the two coordinate components are used as switching statesignals of three phases of the controlled converter, and the controlledconverter is directly controlled by using the space vector of theimagined converter to realize space vector modulation.

It is apparent for those skilled in the art that the present disclosureis not limited to the details of the above exemplary embodiments, andthe present disclosure can be realized in other specific forms withoutdeparting from the spirit or basic characteristics of the presentdisclosure. Therefore, the embodiments should be regarded as beingexemplary and non-limiting from any point of view, and the scope of thepresent disclosure is defined by the appended claims rather than theabove description, so the present disclosure is intended to comprise allchanges falling within the meaning and range of equivalent elements ofthe claims. Any reference numerals in the claims should not be regardedas limiting the claims involved.

What is claimed is:
 1. A simplified space vector modulation method for amulti-level converter, comprising the following steps of: step 1: anexpression of a basic vector V_(αβ)(v_(α),v_(β)) corresponding to aphase voltage in a traditional Cartesian coordinate system (referred toas an α-β coordinate system) being: ${\begin{bmatrix}v_{\alpha} \\v_{\beta}\end{bmatrix} = \begin{bmatrix}{\frac{1}{3}( {{2v_{a}} - v_{b} - v_{c}} )} \\{{\frac{\sqrt{3}}{3}( {v_{b} - v_{c}} )}\mspace{34mu}}\end{bmatrix}},$ wherein v_(α) and v_(β) represent coordinate componentscorresponding to the basic vector V_(αβ), v_(α), v_(b) and v_(c)respectively represent levels corresponding to three phase voltages of amulti-level converter, (v_(a), v_(b), v_(c)) is called a switching statecorresponding to the basic vector V_(αβ), and for an n-level converter,v_(a),v_(b),v_(c) ∈[(n−1), (n−2), . . . , 2, 1, 0]; and a referencevector V_(rαβ)(v_(rα), v_(rβ)) calculated according to phase voltagereference signals in the α-β coordinate system being: ${\begin{bmatrix}v_{r\; \alpha} \\v_{r\; \beta}\end{bmatrix} = {\frac{\sqrt{3}}{3}{{m( {n - 1} )}\begin{bmatrix}{\cos \mspace{14mu} \omega \; t} \\{\sin \mspace{14mu} \omega \; t}\end{bmatrix}}}};$ wherein v_(rα) and v_(rβ) represent coordinatecomponents corresponding to the reference vector V_(rαβ); step 2:rotating a coordinate axis of an α-β plane counterclockwise by 45degrees and compressing an axial proportion to obtain an α′-β′coordinate system, and establishing a reference vector trajectory model;a basic vector V′(v_(α)′,v_(β)′) in the coordinate system α′-β′ being:${\begin{bmatrix}v_{\alpha}^{\prime} \\v_{\beta}^{\prime}\end{bmatrix} = {{\begin{bmatrix}1 & 0 & {- 1} \\{- 1} & 1 & 0\end{bmatrix}\begin{bmatrix}v_{a} \\v_{b} \\v_{c}\end{bmatrix}} = \begin{bmatrix}{{v_{a} - v_{c}}\mspace{20mu}} \\{{- v_{a}} + v_{b}}\end{bmatrix}}},$ wherein v_(α)′ and v_(β)′ represent coordinatecomponents corresponding to the basic vector V′; a reference vectorV_(r′(v) _(rα) ′,v_(rβ)′) calculated according to phase voltagereference signals in the α′-β′ coordinate system being:${\begin{bmatrix}v_{r\; \alpha}^{\prime} \\v_{r\; \beta}^{\prime}\end{bmatrix} = {\frac{m( {n - 1} )}{2}\begin{bmatrix}{{{\sqrt{3}\mspace{14mu} \cos \mspace{14mu} \omega \; t} + {\sin \mspace{14mu} \omega \; t}}\mspace{14mu}} \\{{{- \sqrt{3}}\mspace{14mu} \cos \mspace{14mu} \omega \; t} + {\sin \mspace{14mu} \omega \; t}}\end{bmatrix}}},$ wherein v_(rα)′ and v_(rβ)′ represent coordinatecomponents corresponding to the reference vector V_(r)′; the referencevector trajectory model in the α′-β′ coordinate system being:${{( \frac{v_{r\; \alpha}^{\prime} + v_{r\; \beta}^{\prime}}{m( {n - 1} )} )^{2} + ( \frac{v_{r\; \alpha}^{\prime} - v_{r\; \beta}^{\prime}}{\sqrt{3}{m( {n - 1} )}} )^{2}} = 1};$${m = \frac{\sqrt{3}U_{r}}{( {n - 1} )E}};$ step 3: in theα′-β′ coordinate system, respectively representing line voltagereference signals −u_(rca), u_(rab) and u_(rbc) by the coordinatecomponents v_(rα)′ and v_(rβ)′ of the reference vector V_(r)′ and thesum of the two components v_(rα)′+v_(rβ)′, and respectively representingline voltage level signals −v_(ca), −v_(ab) and v_(bc) by the coordinatecomponents v_(α)′ and v_(β)′ of the basic vector V′ and the sum of thetwo coordinate components v_(α)′+v_(β)′; $\{ {\begin{matrix}{{v_{r\; \alpha}^{\prime} = {{u_{ra} - u_{rc}} = {- u_{rca}}}}\mspace{40mu}} \\{{v_{r\; \beta}^{\prime} = {{{- u_{ra}} + u_{rb}} = {- u_{rab}}}}\mspace{20mu}} \\{{v_{r\; \alpha}^{\prime} + v_{r\; \beta}^{\prime}} = {{u_{rb} - u_{rc}} = u_{rbc}}}\end{matrix},} $ wherein u_(rab), u_(rbc) and u_(rca)respectively the represent reference signals of the three line voltages;${{\begin{bmatrix}{v_{\alpha}^{\prime}\mspace{50mu}} \\{v_{\beta}^{\prime}\mspace{50mu}} \\{v_{\alpha}^{\prime} + v_{\beta}^{\prime}}\end{bmatrix}==\begin{bmatrix}{{v_{a} - v_{c}}\mspace{20mu}} \\{{- v_{a}} + v_{b}} \\{{v_{b} - v_{c}}\mspace{20mu}}\end{bmatrix}} = \begin{bmatrix}{- v_{ca}} \\{- v_{ab}} \\{v_{bc}\mspace{20mu}}\end{bmatrix}},$ wherein v_(ab), v_(bc) and v_(ca) respectivelyrepresent levels corresponding to the three line voltages, v_(ab),v_(bc), v_(ca) ∈[±n, ±(n−1), . . . , ±2, ±1, 0] and each line voltageoutputs 2n+1 levels; step 4: constructing a new star-connectedmulti-level converter, so that line voltage reference signals of the newstar-connected multi-level converter are the same as line voltagereference signals of a controlled delta-connected multi-level converter;step 5: sampling a phase voltage reference vector trajectory model ofthe constructed star-connected multi-level converter, calculating threebasic vectors closest to the sampled reference vector V_(r)′, using thethree basic vectors as equivalent basic vectors, the three equivalentbasic vectors forming a sector triangle, and synthesizing the referencevector by using the three equivalent basic vectors; step 6: calculatingduty cycles of the equivalent basic vectors which synthesize the sampledreference vector by using the volt-second balance principle: when thereference vector is located in Sector-I: $\{ {\begin{matrix}{{t_{1} = {T_{S}( {1 + v_{\alpha}^{\prime} - v_{r\; \alpha}^{\prime}} )}}\mspace{110mu}} \\{{t_{2} = {T_{S}( {1 + v_{\beta}^{\prime} - v_{r\; \beta}^{\prime}} )}}\mspace{110mu}} \\{t_{3} = {T_{S}( {v_{r\; \alpha}^{\prime} + {\, v_{r\; \beta}^{\prime}} - v_{\alpha}^{\prime} - v_{\beta}^{\prime} - 1} )}}\end{matrix},} $ wherein t₁, t₂ and t₃ respectively representduty cycles of vectors V₁′, V₂′ and V₃′, and T_(s) represents thesampling period; when the reference vector is located in Sector-II:$\{ {\begin{matrix}{t_{0} = {T_{S}( {1 + v_{\alpha}^{\prime} + v_{\beta}^{\prime} - v_{r\; \alpha}^{\prime} - v_{r\; \beta}^{\prime}} )}} \\{{t_{1} = {T_{S}( {v_{r\; \alpha}^{\prime} - v_{\alpha}^{\prime}} )}}\mspace{155mu}} \\{{t_{3} = {T_{S}( {v_{r\; \beta}^{\prime} - v_{\beta}^{\prime}} )}}\mspace{149mu}}\end{matrix},} $ wherein t₀, t₁ and t₃ respectively representduty cycles of vectors V₀′, V₁′ and V₃′; and step 7: using thecomponents of the equivalent basic vector of the phase voltage referencevector of the star-connected multi-level converter and the sum of thetwo components as switching states for controlling a line voltage of thedelta-connected multi-level converter.
 2. The simplified space vectormodulation method for the multi-level converter according to claim 1,wherein in step 5, the sector triangles formed by three adjacent basicvectors are all isosceles right triangles, a length of a right side ofthe isosceles right triangle is unit 1, the sector triangles are inSector-I and Sector-II, and the basic vectors forming Sector-I andSector-II comprise V₀′(v_(α)′,v_(β)′), V₁′(v_(α)′+1,v_(β)′),V₂′(v_(α)′+1,v_(β)′+1) and V₃′(v_(α)′,v_(β)′+1), and$\{ {\begin{matrix}{v_{\alpha}^{\prime} = {{floor}( v_{r\; \alpha}^{\prime} )}} \\{v_{\beta}^{\prime} = {{floor}( v_{r\; \beta}^{\prime} )}}\end{matrix},} $ wherein floor(*) represents a rounding downfunction; in a first case: wherein (v_(rα)′−v_(α)′)+(v_(rβ)′−v_(β)′)≥1,the reference vector is located in Sector-I, and the reference vector issynthesized by using the vectors V₁′(v_(α)′+1,v_(β)′),V₂′(v_(α)′+1,v_(β)′+1) and V₃′(v_(α)′,v_(β)′+1); and in a second case:wherein (v_(rα)′−v_(α)′)+(v_(rβ)′−v_(β)′)<1, the reference vector islocated in Sector-II, and the reference vector is synthesized by usingthe vectors V₀′(v_(α)′,v_(β)′), V₁′(v_(α)′+1,v_(β)′) andV₃′(v_(α)′,v_(β)′+1).
 3. The simplified space vector modulation methodfor the multi-level converter according to claim 2, wherein: in thefirst case: when the reference voltage vector V_(r)′ is synthesized byusing V₁′, V₂′ and V₃′ according to volt-second balance principle, theswitching states of the corresponding delta-connected multi-levelconverter are respectively (−v_(β)′,v_(α)′+v_(β)′+1,−(v_(α)′+1)),(−(v_(β)′+1),v_(α)′+2, −(v_(α)′+1)), and (−(v_(β)′+1),v_(α)′+v_(β)′+1,−v_(α)′); (1) during the duty cycle of the basic vector V₁′, −v_(β)′,v_(α)′+v_(β)′+₁ and −(v_(α)′+1) are respectively used as control signalsof a phase AB, a phase BC and a phase CA of the controlleddelta-connected multi-level converter; (2) during the duty cycle of thebasic vector V₂′, −(v_(β)′+1), v_(α)′+v_(β)′+2 and −(v_(α)′+1) arerespectively used as control signals of a phase AB, a phase BC and aphase CA of the controlled delta-connected multi-level converter; (3)during the duty cycle of the basic vector V₃′, −(v_(β)′+1),v_(α)′+V_(β)′+1 and −v_(α)′ are respectively used as control signals ofa phase AB, a phase BC and a phase CA of the controlled delta-connectedmulti-level converter; in the second case: when the reference voltagevector V_(r)′ is synthesized by using V₀′, V₁′ and V₃′ according to thetime-sharing system, the switching states of the correspondingdelta-connected multi-level converter are respectively(−v_(β)′,v_(α)′+v_(β)′,−v_(α)′), (−v_(β)′,v_(α)′+v_(β)′+1,−(v_(α)′+1))and (−(v_(β)′+1),v_(α)′+v_(β)′+1,−v_(α)′); (1) during the duty cycle ofthe basic vector V₀′, −v_(β)′, v_(α)′+v_(β)′ and −v_(α)′ arerespectively used as control signals of a phase AB, a phase BC and aphase CA of the controlled delta-connected multi-level converter; (2)during the duty cycle of the basic vector V₁′, −v_(β)′, v_(α)′+v_(β)+1and −(v_(α)′+1) are respectively used as control signals of a phase AB,a phase BC and a phase CA of the controlled delta-connected multi-levelconverter; (3) during the duty cycle of the basic vector V₃′,−(v_(β)′+1), v_(α)′+v_(β)′+1 and −v_(α)′ are respectively used ascontrol signals of a phase AB, a phase BC and a phase CA of thecontrolled delta-connected multi-level converter.
 4. The simplifiedspace vector modulation method for the multi-level converter accordingto claim 3, wherein a sum of the three components of the switchingstates at any moment is 0, which means that an output common-modevoltage of a three-phase converter is
 0. 5. The simplified space vectormodulation method for the multi-level converter according to claim 3,wherein the switching states are used as the control signals of the linevoltage of the delta-connected multi-level converter, wherein twocomponents of every two of three switching states differ by one level,and during one sampling period of the reference vector, when theswitching states are switched, a switching path is closed by afour-segment switching method with any one of the three switching statesas a starting point, a switching state switching sequence in the firstcase is provided with three modes: mode (1):(−v_(β)′,v_(α)′+v_(β)′+1,−(v_(α)′+1))→(−(v_(β)′+1),v_(α)′+v_(β)′+2,−(v_(α)′+1))→(−v_(β)′+1),v_(α)′+v_(β)′+1,−v_(α)′)→(−v_(β)′,v_(α)′+v_(β)′+1,−(v_(α)′+1)),corresponding to a duty cycle t₁/2→t₂→t₃→t₁/2, mode (2):(−(v_(β)′+1)v_(α)′+v_(β)′+2,−(v_(α)′+1))→(−(v_(β)′+1),v_(α)′+v_(β)′+1,−v_(α)′)→(−v_(β)′,v_(α)′+v_(β)+1,−(v_(α)′+1))→(−v_(β)′+1),v_(α)′+v_(β)′+2,−(v_(α)′+1)),corresponding to a duty cycle t₂/2→t₃→t₁→t₂/2, mode (3):(−(v_(β)′+1),v_(α)′+v_(β)′+1,−v_(α)′)→(−v_(β)′,v_(α)′+v_(β)′+1,−(v_(α)′+1))→(−(v_(β)′+1),v_(α)′+v_(β)′+2,−(v_(α)′+1))→(−(v_(β)′+1),v_(α)′+v_(β)′+1,−v_(α)′)corresponding to a duty cycle t₃/2→t₁→t₂→t₃/2, any one of the threemodes is selected; and the switching state switching sequence in thesecond case is provided with three modes: mode (1):(−v_(β)′,v_(α)′+v_(β)′,−v_(α)′)→(−v_(β)′+v_(α)′+v_(β)′+1,−(v_(α)′+1))→(−(v_(β)′+1),v_(α)′+v_(β)′+1,−v_(α)′)→(−v_(β)′,v_(α)′+v_(β)′,−v_(α)′),corresponding to a duty cycle t₀/2→t₁→t₃→t₀/2, mode (2):(−v_(β)′,v_(α)′+v_(β)′+1,−(v_(α)′+1))→(−(v_(β)′+1),v_(α)′+v_(β)′+1,−v_(α)′)→(−v_(β)′,v_(α)′+v_(β)′,−v_(α)′)→(−v_(β)′,v_(α)′+v_(β)′+1,−(v_(α)′+1)),corresponding to a duty cycle t₁/2→t₃→t₀→t₁/2, mode (3):(−(v_(β)′+1),v_(α)′+v_(β)′+1,−v_(α)′)→(−v_(β)′,v_(α)′+v_(β)′,−v_(α)′)→(−v_(β)′,v_(α)′+v_(β)′+1,−(v_(α)′+1))→(−(v_(β)′+1),v_(α)′+v_(β)′+1,−v_(α)′),corresponding to a duty cycle t₃/2→t₀→t₁→t₃/2, any one of the threemodes is selected.
 6. The simplified space vector modulation method forthe multi-level converter according to claim 1, wherein each phase inthe delta-connected multi-level converter is formed by cascading 2kH-bridge sub-modules, an output line voltage has 4k+1 levels, each phasein the star-connected multi-level converter is formed by cascading kH-bridge sub-modules, an output phase voltage has 2k+1 levels, and anoutput line voltage has 4k+1 levels, which means that a number of levelsof the output line voltage of the star-connected converter formed bycascading k H-bridge sub-modules is equal to a number of levels of theoutput line voltage of the delta-connected converter formed by cascading2k H-bridge sub-modules.
 7. The simplified space vector modulationmethod for the multi-level converter according to claim 1, wherein inthe α′-β′ coordinate system, the star-connected converter formed bycascading 2k H-bridge sub-modules is modulated by the simplifiedmulti-level converter space vector modulation method according to thefollowing steps: step 1: imagining a star-connected converter, whereineach phase of the converter is formed by cascading k H-bridgesub-modules; step 2: dividing the phase voltage reference signals of thecontrolled converter by √{square root over (3)} to obtain phase voltagereference signals of the imaged converter; and step 3: in the α′-β′coordinate system, sampling a phase voltage reference vector trajectorymodel of the imaged converter, synthesizing the reference vector byusing three equivalent basic vectors on the sector triangle, and usingthe coordinate components of the equivalent basic vector and the sum ofthe two coordinate components as switching state signals of three phasesof the controlled converter to realize space vector modulation.